A method and system is provided for rendering bicubic surfaces of an object on a computer system. Each bicubic surface is defined by sixteen control points and bounded by four boundary curves, each corresponding to an edge, and each boundary curve is formed by boundary box of line segments formed between four of the control points. The method and system of include transforming only the control points of the surface given a view of the object, rather than points across the entire bicubic surface, and using the four boundary edges for purposes of subdivision. Next, a pair of orthogonal boundary curves to process is selected. After the boundary curves have been selected, each of the curves is iteratively subdivided and the pair of orthogonal internal curves, wherein two new curves are generated with each subdivision. The subdivision of each of the curves is terminated when the curves satisfy a flatness threshold expressed in screen coordinates, whereby the number of computations required to render the object is minimized.